Super hard M1 question

Particles A and B of mass 2m and m respectively are attached to the ends of a light inextensible string. The string passes over a smooth pulley fixed at the edge of a rough horizontal table. Particle A is held on the table, while B rests on a smooth plane inclined at 30 degrees to the horizontal. The string is in the same vertical plane as a line of greatest slope of the inclined plane. The coefficient of friction between A and the table is miu. The particle A is released from rest and begins to move.

When each particle has moved a distance h, the string breaks. The particle A comes to rest before reaching the pulley. Given that miu = 0.2.

Find, in terms of h, the total distance moved by A.

Help plz... this is super hard.

Reply 1

Sahir

2

Okay i got total distance of A moved = 7h/6 metres;

First of all, obviously draw a diagram, indicating acceleration of both particles and resolve parallel and perpendicular to the surface for both particles A and B:

PARTICLE A:
1) T - 0.2R = 2ma
2) R = 2mg

therefore for particle A; T - 0.4mg = 2ma

PARTICLE B:
1) mg.sin30 - T = ma
2) R = mg.cos30

note that you don't need to use equation 2 because R is irrelevant - the surface on which B rests is SMOOTH

therefore for particle B; mg - 2T = 2ma

Eliminate the 2ma and find T

mg - 2T = T - 0.4mg
1.4mg = 3T

T = 1.4mg/3 = (7mg/15) Newtons

Find initial acceleration (which will be the same for both particles:

T - 0.4mg = 2ma
7mg/15 - 0.4mg = 2ma

a = 49/150 m.s^-2

Find what the velocity of A is when the string breaks and displacement = h

a = 49/150
u = 0
s = h
v = ?

v^2 = u^2 + 2as
v^2 = 49h/75

Draw another diagram, just for particle A once the string has broke and there is no tension / driving force and resolve:

-0.2(2mg) = 2ma
a = -0.2g

use v^2 = u^2 + 2as again..

from before.. u^2 = 49h/75
v = 0
a = -0.2g
s = ?

v^2 = 0 = 49h/75 + 2(-0.2g)s

s = (49h/75) / 0.4g = h/6 metres AFTER THE STRING HAS BROKEN

Total displacement = h + h/6 = 7h/6 metres!

Btw.. that took fking ages!

Reply 2

stanny

OP

wow thx LOADS ^^

Reply 3

Sahir

2

stanny

wow thx LOADS ^^

You're v welcome mate

Reply 4

stanny

OP

no wonder... this was from the paper that my bro did and he got the highest in class, which was only 85... the q's were esp hard... somehow

Reply 5

stanny

OP

ppl here are too smart i guess

Reply 6

john !!

14

That's not harder than the average question, it's just a lot longer. With a diagram and some time anyone studying M1 could do that... you usually get a question like that at the last question anyway, where it asks about how far a particle has travelled after a force is removed.

Reply 7

Sahir

2

mik1a

That's not harder than the average question, it's just a lot longer. With a diagram and some time anyone studying M1 could do that... you usually get a question like that at the last question anyway, where it asks about how far a particle has travelled after a force is removed.

Also helps that i'm resitting M1 this year after having finished M2 aswell, and i feel a lot more comfortable with mechanics this year.. just used to it i guess!

Don't worry bout it, that'd be the longest question on the paper by far.. just think logically and work through it..!